Crystallisation method with control of the orientation of the crystal grains

ABSTRACT

A crystallization method, including: depositing a thin film of a crystalline material on a substrate; heating the substrate and the crystalline material deposited on the substrate to a first temperature for a time enabling internal strains present in the crystalline material to be relaxed; after the heating, subjecting the substrate and the crystalline material to a second temperature and to a uniform bending by placing the substrate on a bending bench, a quantity of bending and a difference between the first and the second temperature having values determined from elastic bending constants, thermal deformations and thermal expansion coefficients to favor a particular crystallographic orientation of the crystalline material along an azimuth direction in relation to a direction normal to the substrate.

The invention relates to a crystallisation method, the essential featureof which is that the orientation of the crystal grains is controlled.

The orientation of the grains of the crystal is decided during itsgrowth under the effect of numerous and complex phenomena, whichmoreover depend on the method used. Since the properties of thematerials depend in general on the orientation of the grains, it may beuseful to control said orientation. This concerns in particularelectrical conductivity properties in thin films of copper or otherconductive materials used in integrated circuits. In addition, it isoften worthwhile maintaining a same crystallographic orientation of thegrains over a large area of the crystal.

The prior art includes a certain number of works attempting to elucidatethe mechanisms influencing the orientation of crystals, but it does notseem that a simple and general method of controlling the orientation ofthe grains has been proposed in the particular case of thin films at thesurface of a substrate.

The fundamental object of the invention is to fill this gap. It relatesto a crystallisation method, consisting in depositing at least partiallythe material of the crystal on a substrate in a thin film, heating thesubstrate and the material deposited on a substrate to a firsttemperature for a time enabling the internal strains present in thedeposited material to be relaxed, then subjecting the substrate and saiddeposited material to a second temperature and to a uniform bending byplacing the substrate on a bending bench, a quantity of bending and adifference between the first and the second temperatures having valuesdetermined from relations bringing into play elastic bending constants,thermal deformations and thermal expansion coefficients to favour aparticular crystallographic orientation of the material deposited alongan azimuth direction in relation to a direction normal to the substrate,by a simple rearrangement of the material.

BRIEF DESCRIPTION OF DRAWING

FIG. 1 is a schematic of a device for implementation of strain to asubstrate.

DETAILED DESCRIPTION OF THE INVENTION

The invention will now be described by means of FIG. 1, which representsthe device used for the implementation of the method. It involves afurnace 1 including a bending bench 2. A substrate 3 coated with a layer4 of the material of the crystal is enclosed therein. According to theinvention, a thin film is of thickness such that the deformationsparallel to the surface of the substrate 3 are fully communicated tosaid layer over its whole thickness. In a first step, the substrate 3and the layer 4 are heated to a uniform temperature for a time enablingthe internal strains therein to be relaxed, since these internal strainswould perturb the implementation of the method and they are generallyhigh following the usual deposition methods. The applied temperaturemust however leave the material of the layer 4 solid. It may be around300° C. for deposits of electrolytic copper on silicon substrates usedfor the elaboration of integrated circuits, and determined bycalculation or by X-ray diffraction measurements.

A temperature difference, defined in relation to the previoustemperature, is then applied to the substrate 3 and to the layer 4 atthe same time as a bending by the bench 2. Strains of dual origin,bending and thermal expansion, appear. Their effects in the crystallinematerial of the layer 4 will now be explained by means of the mechanicsof continuous media.

Beginning with the relation (1) ε total=ε applied+ε elastic, whichexpresses that, in the layer 4, the total deformations are the sum ofthe deformations applied by the external medium and internal elasticdeformations. In the case of a cubic crystal, the system of equations(2) is obtained:

$\underset{\underset{\underset{\_}{\_}}{ɛ}\mspace{14mu}{total}}{\begin{pmatrix}\beta_{1} & 0 & 0 \\0 & \beta_{2} & 0 \\0 & 0 & \beta\end{pmatrix}} = {\underset{\underset{\underset{\_}{\_}}{ɛ}\mspace{14mu}{applied}}{\begin{pmatrix}\alpha & 0 & 0 \\0 & \alpha & 0 \\0 & 0 & \alpha\end{pmatrix}} + \underset{\underset{\underset{\_}{\_}}{ɛ}\mspace{14mu}{elastic}}{\begin{pmatrix}ɛ_{11}^{e} & ɛ_{12}^{e} & ɛ_{13}^{e} \\ɛ_{12}^{e} & ɛ_{22}^{e} & ɛ_{23}^{e} \\ɛ_{13}^{e} & ɛ_{23}^{e} & ɛ_{33}^{e}\end{pmatrix}}}$in the principal mark defined by the vectors x₁, x₂ and x₃, where x₁ isin the length of the substrate 3 (along the applied curve), x₂ in thewidth and x₃ is normal to the surface on which the layer 4 has beendeposited. The total deformations comprise three components, the firsttwo of which are defined by the deformations on the upper face of thesubstrate 3 since the substrate 3, very thick compared to the layer 4,imposes on it its deformations, and are linked by the equation:β₂=−νβ₁,  (3)ν being the Poisson coefficient of the substrate.The α components of the deformations applied are due to thermalexpansions and depend on the corresponding coefficients. The thermalexpansion of the substrate 3 is disregarded in the followingcalculations, but it can easily be taken into account by a modificationof the total deformations, since this thermal expansion of the substrate3 amounts to a condition at the limits. Furthermore, the componentsε_(ij) represent the elastic deformations of the layer 4.

A new mark linked to the crystal is now introduced, formed of vectorsy₁, y₂ and y₃, and vectors q′, q″ and q, which are unitary vectorsidentical to the vectors x₁, x₂ and x₃, but which are defined from thepoint of view of the layer 4. The coordinates of the directions q, q′and q″ in the mark (y₁, y₂ y₃) are noted q₁, q₂ and q₃; q′₁, q′₂ andq′₃; q″₁, q″₂, and q″₃ respectively.

In the mark (y₁, y₂, y₃), the components ε^(e) ₁₁, ε^(e) ₂₂, ε^(e) ₃₃,ε^(e) ₂₃, ε^(e) ₁₃ and ε^(e) ₁₂ of (2), expressed in matrix notation e₁to e₆, are equal to:e ₁=−α+β₁ Q′ ₁+β₂ Q″ ₁ +βQ ₁e ₂=−α+β₁ Q′ ₂+β₂ Q″ ₂ +βQ ₂e ₃=−α+β₁ Q′ ₃+β₂ Q″ ₃ +βQ ₃e ₄=2β₁ Q′ ₄+2β₂ Q″ ₄+2βQ ₄e ₅=2β₁ Q′ ₅+2β₂ Q″ ₅+2βQ ₅e ₆=2β₁ Q′ ₆+2β₂ Q″ ₆+2βQ ₆  (4)with Q₁=q₁ ², Q₂=q₁ ², Q₃=q₃ ², Q₄=q₂q₃, Q₅=q₃q₁, Q₆=q₁q₂, and likewisefor the expressions of Q′ and Q″.

Hooke's law σ=Cε, general and valid in the elastic domain ofdeformations, makes it possible to determine the strains tensor andparticularly the strains vector σ(q) that applies on the free surface ofthe layer 4. This gives the system of components (5) expressed in themark linked to the crystal:along y ₁: [−(C ₁₁+2C ₁₂)α+(AQ ₁ +C ₁₂)β+(AQ″ ₁ +C ₁₂)δ+2Aq ₁ q″ ₁ γ]q′₁along y ₂: [−(C ₁₁+2C ₁₂)α+(AQ ₂ +C ₁₂)β+(AQ″ ₂ +C ₁₂)δ+2Aq ₂ q″ ₂ γ]q′₂along y ₃: [−(C ₁₁+2C ₁₂)α+(AQ ₃ +C ₁₂)β+(AQ″ ₃ +C ₁₂)δ+2Aq ₃ q″ ₃ γ]q′₃

The components C_(ij) are those of the tensor of the elastic constantsof the crystal considered:

$\begin{matrix}\begin{pmatrix}C_{11} & C_{12} & C_{12} & 0 & 0 & 0 \\C_{12} & C_{11} & C_{12} & 0 & 0 & 0 \\C_{12} & C_{12} & C_{11} & 0 & 0 & 0 \\0 & 0 & 0 & C_{44} & 0 & 0 \\0 & 0 & 0 & 0 & C_{44} & 0 \\0 & 0 & 0 & 0 & 0 & C_{44\;}\end{pmatrix} & (6)\end{matrix}$

Yet the components of the system (5) must all be zero since the strainapplying on a free surface is also zero. By adding these componentsmember by member and by noting that the relations (7):Q ₁ +Q ₂ +Q ₃=1,Q′ ₁ +Q′ ₂ +Q′ ₃=1 and Q″ ₁ +Q″ ₂ +Q″ ₃=1

-   -   apply, the vectors q, q′ and q″ being normal, finally the        relation (8) is obtained:        −3(C ₁₁+2C ₁₂)α+(A+3C ₁₂)(β₁+β₂)+(A+3C ₁₂+6C ₄₄)β=0    -   between α, β₁ and β, which is independent of the choice of q, q′        and q″.

By using this relation in the mark linked to the crystal, the system (5)of components becomes the system (9):

${along}\mspace{14mu} y_{1}\text{:}\mspace{14mu}{A\left\lbrack {{\left( {Q_{1}^{\prime} - \frac{1}{3}} \right)\beta_{1}} + {\left( {Q_{1}^{''} - \frac{1}{3}} \right)\beta_{2}} + {\left( {Q_{1} - \frac{1}{3}} \right)\beta}} \right\rbrack}q_{1}$${along}\mspace{14mu} y_{2}\text{:}\mspace{14mu}{A\left\lbrack {{\left( {Q_{2}^{\prime} - \frac{1}{3}} \right)\beta_{1}} + {\left( {Q_{2}^{''} - \frac{1}{3}} \right)\beta_{2}} + {\left( {Q_{2} - \frac{1}{3}} \right)\beta}} \right\rbrack}q_{2}$with  β₂ = −v β₁${along}\mspace{14mu} y_{3}\text{:}\mspace{14mu}{A\left\lbrack {{\left( {Q_{3}^{\prime} - \frac{1}{3}}\; \right)\beta_{1}} + {\left( {Q_{3}^{''} - \frac{1}{3}} \right)\beta_{2}} + {\left( {Q_{3} - \frac{1}{3}} \right)\beta}} \right\rbrack}q_{3}$

-   -   to express the strain applying on the free surface of the layer        4 with A=C₁₁−C₁₂−2C₄₄.

The free surface condition σ(q)=0 is necessarily respected if thecrystal is isotropic, since then A=0. Common crystalline materials havehowever in practice a degree of anisotropy, in such a way that it is thequantities in square brackets of the system (9) that must be zero.

The use of relations (7) makes it possible to simplify the system (9)and to obtain the system of equations (10):

$\left\{ {\quad\begin{matrix}{{{\left( {Q_{1}^{\prime} - \frac{1}{3}} \right)\left( {\beta_{1} - \beta_{2}} \right)} + {\left( {Q_{1} - \frac{1}{3}} \right)\left( {\beta - \beta_{2}} \right)}} = 0} \\{{{\left( {Q_{2}^{\prime} - \frac{1}{3}} \right)\left( {\beta_{1} - \beta_{2}} \right)} + {\left( {Q_{2} - \frac{1}{3}} \right)\left( {\beta - \beta_{2}} \right)}} = 0} \\{{{\left( {Q_{3}^{\prime} - \frac{1}{3}} \right)\left( {\beta_{1} - \beta_{2}} \right)} + {\left( {Q_{3} - \frac{1}{3}} \right)\left( {\beta - \beta_{2}} \right)}} = 0}\end{matrix}} \right.$

It only allows a solution for certain values of q and q′ on account oforthogonality and normality strains of the vectors. In other words, theapplication of a bending deformation to the substrate 3 combined with adeformation of thermal origin of the layer 4 makes it possible on theone hand to limit the possible orientations of the crystal and on theother hand to direct it in azimuth since the expression of thecoordinates of q′ is determined by that of q.

Certain particular cases may be discerned. If q is parallel to thedirection [111], Q₁=Q₂=Q₃=½, and from this is deduced Q′₁=Q′₂=Q′₃=⅓, inother words that q′ is also parallel to [111] and thus merged with q,which is impossible. It is deduced from this that an anisotropicmonocrystal from the elastic point of view cannot adopt a direction ofgrowth of direction [111] from the moment that the substrate 3 is bent.This result is valid when the system of components (6) can be used, inother words for crystals with cubic symmetry; it should be noted that inthe absence of bending, the direction of growth [111] is possible, justas are the directions of growth [110] and [100].

In a second particular case, β₁ and α is chosen so that β=β2 ₂ Thesystem (10) gives as solution Q′₁=Q′₂=Q′₃=⅓, and q is indeterminate. q′is thus of direction [111]. The monocrystal has an axis [111] parallelto the direction x₁.

In a third case, β₁ and α are chosen so that β=β₁, conversely one hasQ″₁=Q″₂=Q″₃=⅓, and q still indeterminate. q″ is thus of direction [111].The monocrystal has an axis [111] parallel to the direction x₂. Thesetwo latter examples show that the crystals may be directed in azimutharound the direction x₃ orthogonal to the layer 4 according to thechoices of β₁ and α.

In the case of a layer of copper having a Poisson coefficient ν=0.33, ofelastic constants C₁₁=169 GPa, C₁₂=122 GPa, C₄₄=76 GPa and a thermalexpansion coefficient equal to 16.10⁻⁶ K⁻¹, if the substrate is bent sothat β₁=3.10⁻³, the condition β=β₁ of the third particular case isobtained for α=2.16.10⁻³ i.e. ΔT=+135° C. and the condition β₂ of thesecond particular case for α=−0.156.10⁻³ i.e. ΔT=−10° C.

Other orientations in azimuth may be obtained with other temperaturevariations. The previous results have been obtained for situations whereq1, q2 and q3 are all three non-zero. The vector q could have one or twozero components, and similar results would still be obtained. If forexample q₃=0 and q₁≠q₂, if β1 and α are chosen so that β=β2, q′ is thedirection [001] and q (⊥ q′) is indifferent. The axis [001] of thecrystals is then oriented in the direction x₁. Likewise, if β=β₁, q″ isof direction [001] and the corresponding axis of the crystal is in thedirection x₂.

The previous results may be extrapolated to other crystals, the systemsbeing only more complicated since the elasticity tensor then has lesszero components C_(ij) than the system (6). For example, the tensor of amonoclinic system is given by the system (11):

$\quad\begin{pmatrix}C_{11} & C_{12} & C_{13} & 0 & C_{15} & 0 \\C_{12} & C_{22} & C_{23} & 0 & C_{25} & 0 \\C_{13} & C_{23} & C_{33} & 0 & C_{35} & 0 \\0 & 0 & 0 & C_{44} & 0 & C_{46} \\C_{15} & C_{25} & C_{35} & 0 & C_{55} & 0 \\0 & 0 & 0 & C_{46} & 0 & C_{66}\end{pmatrix}$

In all cases, it is possible to direct the network of the crystal inazimuth around the direction orthogonal to the crystalline layeraccording to the corresponding temperature and bending.

The device should cover quite a wide temperature range, typicallybetween ambient and 500° C. The bending bench 2 could be dimensioned toinduce deformations of the order of several thousandths. The furnace 1should be under vacuum or under neutral gas so as to avoid the oxidationof the treated layers.

The invention claimed is:
 1. A crystallisation method, comprising: depositing a thin film of a conductive crystalline material on a substrate; heating the substrate and the crystalline material deposited on the substrate to a first temperature for a time enabling internal strains present in the crystalline material to be relaxed; after the heating, subjecting the substrate and said crystalline material to a second temperature and to a uniform bending by placing the substrate on a bending bench, a quantity of bending and a difference between the first and the second temperature having values determined from elastic bending constants thermal deformations and thermal expansion coefficients to favour a particular crystallographic orientation of the crystalline material along an azimuth direction in relation to a direction normal to the substrate which is defined by the system of equations: $\quad\left\{ \begin{matrix} {{{\left( {Q_{1}^{\prime} - \frac{1}{3}} \right)\left( {\beta_{1} - \beta_{2}} \right)} + {\left( {Q_{1} - \frac{1}{3}} \right)\left( {\beta - \beta_{2}} \right)}} = 0} \\ {{{\left( {Q_{2}^{\prime} - \frac{1}{3}} \right)\left( {\beta_{1} - \beta_{2}} \right)} + {\left( {Q_{2} - \frac{1}{3}} \right)\left( {\beta - \beta_{2}} \right)}} = 0} \\ {{{\left( {Q_{3}^{\prime} - \frac{1}{3}} \right)\left( {\beta_{1} - \beta_{2}} \right)} + {\left( {Q_{3} - \frac{1}{3}} \right)\left( {\beta - \beta_{2}} \right)}} = 0} \end{matrix} \right.$ where β₁, β₂, and β are total deformations underwent by the film in length, corresponding to a curvature related to the bending, width, and thickness directions in the film, and Q₁, Q₂, Q₃, Q′₁, Q′₂, Q′₃ are equal to q₁ ², q₂ ², q₃ ², q′₁ ², q′2 ², q′₃ ², respectively, where q₁, q₂, and q₃ are coordinates of unitary vectors (x₁ and a₂) oriented in said length and width directions, impressed in a reference (y₁, y₂, and y₃) of the crystal.
 2. The method of claim 1, wherein the crystalline material is copper.
 3. The method of claim 1, wherein the crystalline material is a conductive material used in integrated circuits. 